1. A square ABCD is inscribed in a circle of unit radius. Semicircles are described on each side of a diameter. The area of the region bounded by the four semicircles and the circle is





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  • By: anil on 05 May 2019 01.55 am
    Radius of the circle = 1 unit, => Diameter = BD = 2 units Thus, side of square = AB = $$sqrt2$$ units Radius of a semi-circle = $$frac{AB}{2}=frac{sqrt2}{2}=frac{1}{sqrt2}$$ => Area of 4 semi-circles = $$2pi r^2$$ = $$2pi (frac{1}{sqrt2})^2=pi$$ sq. units ------------(i) Area bounded by region = Area of circle - Area of square = $$pi(1)^2-(sqrt2)^2=(pi-2)$$ sq. units ---------------(ii) $$ herefore$$ Required area bounded by 4 semi circles = (i) - (ii) = $$pi - (pi-2) = 2$$ sq. units => Ans - (B)
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